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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>3</sub></font> being  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><a NAME="E1:40"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 <b>and </b><br/><a NAME="E2:40"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>1</sub></font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 ;<br/>

<a NAME="E3:40"/><i><font color="Green">E37</font></i>: 
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="waybel13.html#E2:40"><i><font color="Green">E36</font></i></a>, <a class="ref" href="waybel_1.html#T7">WAYBEL_1:7</a></i>;<br/>
<a NAME="E4:40"/><i><font color="Green">E38</font></i>: 
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font> is  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:40"><i><font color="Green">E35</font></i></a>, <a class="ref" href="yellow_2.html#T37">YELLOW_2:37</a></i>;<br/>
<a NAME="E5:40"/>
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font> is  <a href="waybel_8.html#V2">algebraic</a> <a href="waybel_0.html#NM8">LATTICE</a>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:40"><i><font color="Green">E35</font></i></a>, <a class="ref" href="waybel_8.html#T26">WAYBEL_8:26</a></i>;<br/>
<b>hence </b><a NAME="E6:40"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_8.html#V2">algebraic</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E3:40"><i><font color="Green">E37</font></i></a>, <a class="txt" href="waybel13.html#E4:40"><i><font color="Green">E38</font></i></a>, <a class="ref" href="waybel13.html#T32" target="_self">Th32</a></i>;<br/>


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